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The Beauty of Mathematics in Computer Science

By

Jun Wu





ISBN 9781138049604
Published November 5, 2018 by Chapman and Hall/CRC
268 Pages

 
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Book Description

The Beauty of Mathematics in Computer Science explains the mathematical fundamentals of information technology products and services we use every day, from Google Web Search to GPS Navigation, and from speech recognition to CDMA mobile services. The book was published in Chinese in 2011 and has sold more than 600,000 copies. Readers were surprised to find that many daily-used IT technologies were so tightly tied to mathematical principles. For example, the automatic classification of news articles uses the cosine law taught in high school.

The book covers many topics related to computer applications and applied mathematics including:

Natural language processing

Speech recognition and machine translation

Statistical language modeling

Quantitive measurement of information

Graph theory and web crawler

Pagerank for web search

Matrix operation and document classification

Mathematical background of big data

Neural networks and Google’s deep learning

Jun Wu was a staff research scientist in Google who invented Google’s Chinese, Japanese, and Korean Web Search Algorithms and was responsible for many Google machine learning projects. He wrote official blogs introducing Google technologies behind its products in very simple languages for Chinese Internet users from 2006-2010. The blogs had more than 2 million followers. Wu received PhD in computer science from Johns Hopkins University and has been working on speech recognition and natural language processing for more than 20 years. He was one of the earliest engineers of Google, managed many products of the company, and was awarded 19 US patents during his 10-year tenure there. Wu became a full-time VC investor and co-founded Amino Capital in Palo Alto in 2014 and is the author of eight books.

Table of Contents

1. Words and languages, numbers and information
   Information
   Words and numbers
   The mathematics behind language

2. Natural language processing|From rules to statistics
   Machine intelligence
   From rules to statistics

3. Statistical language model
   Describing language through mathematics
   Extended reading: Implementation caveats
   Higher order language models
   Training methods, zero-probability problems, and smoothing
   Corpus selection

4. Word segmentation
   Evolution of Chinese word segmentation
   Extended reading: evaluating results
   Consistency
   Granularity

5. Hidden Markov model
   Communication models
   Hidden Markov model
   Extended reading: HMM training

6. Quantifying information
   Information entropy
   Role of information
   Mutual information
   Extended reading: Relative entropy

7. Jelinek and modern language processing
   Early life
   From Watergate to Monica Lewinsky
   An old man's miracle

8. Boolean algebra and search engines
   Boolean algebra
   Indexing

9. Graph theory and web crawlers
   Graph theory
   Web crawlers
   Extended reading: two topics in graph theory
   Euler's proof of the Königsberg bridges
   The engineering of a web crawler

10.PageRank: Google's democratic ranking technology
   The PageRank algorithm
   Extended reading: PageRank calculations

11.Relevance in web search
   TF-IDF
   Extended reading: TF-IDF and information theory

12.Finite state machines and dynamic programming: Navigation in Google Maps
   Address analysis and Finite state machines
   Global navigation and dynamic programming
   Finite state transducer

13.Google's AK- designer, Dr Amit Singhal

14.Cosines and news classification
   Feature vectors for news
   Vector distance
   Extended reading: The art of computing cosines
   Cosines in big data
   Positional weighting

15.Solving classification problems in text processing with matrices
   Matrices of words and texts
   Extended reading: Singular value decomposition method and applications

16.Information Fingerprinting and its application
   Information Fingerprint
   Applications of information Fingerprint
   Determining identical sets
   Detecting similar sets
   YouTube's anti-piracy
   Extended reading: Information Fingerprint's repeatability and SimHash
   Probability of repeated information Fingerprint
   SimHash

17.Thoughts inspired by the Chinese TV series Plot: The mathematical principles of cryptography
   The spontaneous era of cryptography
   Cryptography in the information age

18.Not all that glitters is gold: Search engine's anti-SPAM problem and search result authoritativeness question
   Search engine anti-SPAM
   Authoritativeness of search results
   Summary

19.Discussion on the importance of mathematical models

20.Don't put all your eggs in one basket: The principle of maximum entropy
   Principle of maximum entropy and maximum entropy model
   Extended reading: Maximum entropy model training

21.Mathematical principles of pinyin input method
   Input method and coding
   How many keystrokes to type a Chinese character?
   Discussion on Shannon's First Theorem
   The algorithm of phonetic transcription
   Extended reading: Personalized language models

22.Bloom Filters
   The principle of Bloom Filters
   Extended reading: The false alarm problem of Bloom Filters

23.Bayesian network: Extension of Markov Chain
   Bayesian network
   Bayesian network's application in word classification
   Extended reading: Training a Bayesian network

24.Conditional random Fields, syntactic parsing, and more
   Syntactic parsing|the evolution of computer algorithms
   Conditional random fields
   Conditional random fields' applications in other fields

25.Andrew Viterbi and the Viterbi Algorithm
   The Viterbi algorithm
   CDMA technology: The foundation of G mobile communication

26.God's algorithm: The expectation maximization algorithm
   Self-converged document classification
   Extended reading: Convergence of expectation-maximization algorithms

27.Logistic regression and web search advertisement
   The evaluation of web search advertisement
   The logistic model

28.Google Brain and artificial neural networks
   Artificial neural network
   Training an artificial neural network
   The relationship between artificial neural networks and
   Bayesian networks
   Extended reading: \Google Brain"

29.The power of big data
   The importance of data
   Statistics and information technology
   Why we need big data

...
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Author(s)

Biography

Jun Wu was a staff research scientist in Google who invented Google’s Chinese, Japanese, and Korean Web Search Algorithms and was responsible for many Google machine learning projects. He wrote official blogs introducing Google technologies behind its products in very simple languages for Chinese internet users from 2006-2010. The blogs had more than two million followers. He received Ph.D. in computer science from the Johns Hopkins University and had been working on speech recognition and natural language processing for more than 20 years. He was one of the earliest engineers of Google, managed many products of the company, and was awarded more than ten US patents during his ten-year tenure there. He became a full-time VC investor and co-founded Amino Capital in Palo Alto in 2014 and is the author of eight books.

Reviews

"This volume originates from a series of blog articles by the author, who works as senior staff research scientist for Google China. The blog articles have been rewritten to make them more accessible to uninitiated readers. As a result, the book contains 29 chapters which may be read independently. The aim is to provide evidence for the beauty of mathematics and the wealth of its applications to the layman . . . The volume may be quite valuable for readers who want to get some insight into how enterprises like Google achieve their performance, and how much mathematics is at work in the background of many commonplace services . . . "

~Dieter Riebesehl (Lüneburg), zbMath